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If P^2 + Q^2 =1, is P – Q =1?
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25 Aug 2012, 05:32
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If P^2 + Q^2 =1, is P – Q =1? (1) P + Q = 1 (2) P is a positive integer.
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Re: If P^2 + Q^2 =1, is P – Q =1?
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25 Aug 2012, 05:41
If P^2 + Q^2 =1, is P – Q =1?(1) P + Q = 1 > if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient. (2) P is a positive integer > since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether PQ=1 is YES. Sufficient. Answer: B.
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Re: If P^2 + Q^2 =1, is P – Q =1?
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Updated on: 25 Aug 2012, 05:57
Bunuel wrote: If P^2 + Q^2 =1, is P – Q =1?
(1) P + Q = 1 > if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.
(2) P is a positive integer > since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether PQ=1 is YES. Sufficient.
Answer: B. Should be P  Q, but this doesn't really change anything in the answer. After you correct your post, you can erase mine.
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Originally posted by EvaJager on 25 Aug 2012, 05:52.
Last edited by EvaJager on 25 Aug 2012, 05:57, edited 1 time in total.



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Re: If P^2 + Q^2 =1, is P – Q =1?
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25 Aug 2012, 05:56
Thanks Bunuel! Silly question but i will still ask.How can we be sure that Q is also an integer? We have not been given any info on Q.



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Re: If P^2 + Q^2 =1, is P – Q =1?
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25 Aug 2012, 06:01
shivanigs wrote: Thanks Bunuel! Silly question but i will still ask.How can we be sure that Q is also an integer? We have not been given any info on Q. No need for Q to be an integer. Since P = 1, it comes out that Q = 0 (from \(P^2+Q^2=1\)).
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Re: If P^2 + Q^2 =1, is P – Q =1?
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25 Aug 2012, 06:04
shivanigs wrote: Thanks Bunuel! Silly question but i will still ask.How can we be sure that Q is also an integer? We have not been given any info on Q. Do you mean for (2)? Here, since we determined that P=1 we can solve P^2+Q^2=1 to get the value of Q: 1^2+Q^2=1 > Q=0. EvaJager wrote: Bunuel wrote: If P^2 + Q^2 =1, is P – Q =1?
(1) P + Q = 1 > if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.
(2) P is a positive integer > since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether PQ=1 is YES. Sufficient.
Answer: B. Should be P  Q, but this doesn't really change anything in the answer. After you correct your post, you can erase mine. If the first statement were PQ=1, then it would be sufficient, since that's exactly what we are asked  to find whether PQ=1.
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Re: If P^2 + Q^2 =1, is P – Q =1?
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25 Aug 2012, 06:15
Bunuel wrote: shivanigs wrote: Thanks Bunuel! Silly question but i will still ask.How can we be sure that Q is also an integer? We have not been given any info on Q. Do you mean for (2)? Here, since we determined that P=1 we can solve P^2+Q^2=1 to get the value of Q: 1^2+Q^2=1 > Q=0. EvaJager wrote: Bunuel wrote: If P^2 + Q^2 =1, is P – Q =1?
(1) P + Q = 1 > if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.
(2) P is a positive integer > since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether PQ=1 is YES. Sufficient.
Answer: B. Should be P  Q, but this doesn't really change anything in the answer. After you correct your post, you can erase mine. If the first statement were PQ=1, then it would be sufficient, since that's exactly what we are asked  to find whether PQ=1. OMG...I'm an astronaut today...
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Re: If P^2 + Q^2 =1, is P – Q =1?
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21 Oct 2013, 11:46
EvaJager wrote: shivanigs wrote: Thanks Bunuel! Silly question but i will still ask.How can we be sure that Q is also an integer? We have not been given any info on Q. No need for Q to be an integer. Since P = 1, it comes out that Q = 0 (from \(P^2+Q^2=1\)). hi, not sure, if iota (i) concept can be applied in here .. i thought, in verifying S2, P=2, Q^2=3, Q=sqrt3 * iota so, in this case also, p^2+Q^2=1



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Re: If P^2 + Q^2 =1, is P – Q =1?
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06 Feb 2016, 13:17
Hi BunuelCan you please tell me why A cant be sufficient using below approach? Given P^2 + Q^2 = 1. PQ = 1 => SQUARING BOTH SIDES => P^2 + Q^2 2PQ = 1 => 1 2PQ = 1 (SUBSTITUTING THE VALUE OF P^2 + Q^2) => PQ = 0 So our question becomes whether one of p or q is zero? Now looking at A : P+Q = 1 => Squaring both sides => P^2 + Q^2 + 2PQ = 1 => 1+2PQ = 1 ( SUBSTITUTING THE VALUE OF P^2 + Q^2) => PQ = 0 So this should be sufficient right? Bunuel wrote: If P^2 + Q^2 =1, is P – Q =1?
(1) P + Q = 1 > if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.
(2) P is a positive integer > since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether PQ=1 is YES. Sufficient.
Answer: B.



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Re: If P^2 + Q^2 =1, is P – Q =1?
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07 Feb 2016, 04:34
neeraj609 wrote: Hi BunuelCan you please tell me why A cant be sufficient using below approach? Given P^2 + Q^2 = 1. PQ = 1 => SQUARING BOTH SIDES => P^2 + Q^2 2PQ = 1 => 1 2PQ = 1 (SUBSTITUTING THE VALUE OF P^2 + Q^2) => PQ = 0 So our question becomes whether one of p or q is zero? Now looking at A : P+Q = 1 => Squaring both sides => P^2 + Q^2 + 2PQ = 1 => 1+2PQ = 1 ( SUBSTITUTING THE VALUE OF P^2 + Q^2) => PQ = 0 So this should be sufficient right? Bunuel wrote: If P^2 + Q^2 =1, is P – Q =1?
(1) P + Q = 1 > if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.
(2) P is a positive integer > since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether PQ=1 is YES. Sufficient.
Answer: B. You cannot square. If p  q = 1, then (p  q)^2 would be equal to 1^2 but p  q = 1 is not equal to 1.
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Re: If P^2 + Q^2 =1, is P – Q =1?
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16 Mar 2019, 04:39
Bunuel wrote: If P^2 + Q^2 =1, is P – Q =1?
(1) P + Q = 1 > if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.
(2) P is a positive integer > since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether PQ=1 is YES. Sufficient.
Answer: B. Hi, Any reason why we shouldn't rephrase the question ?
PQ=1? => squaring both the sides => p^2+q^22pq=1 => since P^2 +Q^2 =1 => 2pq=0 => pq =0 ?????




Re: If P^2 + Q^2 =1, is P – Q =1?
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